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Bootstrap confidence intervals in nonparametric regression with built-in bias correction

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  • McMurry, Timothy L.
  • Politis, Dimitris N.

Abstract

The problem of estimating nonparametric regression with associated confidence intervals is addressed. It is shown that through appropriate choice of infinite order kernel, it is possible to construct bootstrap confidence intervals which do not require either explicit bias correction or suboptimal levels of smoothing at any stage of the estimation. In particular, it is demonstrated that in this setting, consistent estimates are obtained when both the pilot and final smoothings are estimated at the mean square error optimal bandwidth for estimating the regression. The effectiveness of the method is demonstrated through a small simulation study.

Suggested Citation

  • McMurry, Timothy L. & Politis, Dimitris N., 2008. "Bootstrap confidence intervals in nonparametric regression with built-in bias correction," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2463-2469, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2463-2469
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    References listed on IDEAS

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    1. Politis, Dimitris N. & Romano, Joseph P., 1999. "Multivariate Density Estimation with General Flat-Top Kernels of Infinite Order," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 1-25, January.
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    Cited by:

    1. Michael G. Arghyrou & Maria Dolores Gadea, 2019. "Private bank deposits and macro/fiscal risk in the euro-area," CESifo Working Paper Series 7532, CESifo.
    2. Peter Hall & Joel L. Horowitz, 2012. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers 14/12, Institute for Fiscal Studies.
    3. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Peter Hall & Joel L. Horowitz, 2012. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP14/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Dimitris Politis, 2013. "Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 183-221, June.
    6. Joel L. Horowitz & Anand Krishnamurthy, 2017. "A bootstrap method for constructing pointwise and uniform confidence bands for conditional quantile functions," CeMMAP working papers CWP01/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Violetta Dalla & Liudas Giraitis & Hira L. Koul, 2014. "Studentizing Weighted Sums Of Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 151-172, March.
    8. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers 29/13, Institute for Fiscal Studies.
    9. Politis, Dimitris N, 2010. "Model-free Model-fitting and Predictive Distributions," University of California at San Diego, Economics Working Paper Series qt67j6s174, Department of Economics, UC San Diego.
    10. Joel L. Horowitz & Anand Krishnamurthy, 2017. "A bootstrap method for constructing pointwise and uniform confidence bands for conditional quantile functions," CeMMAP working papers 01/17, Institute for Fiscal Studies.

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